ABSTRACT:

We cast natural-image segmentation as a problem of clustering texure
features as multivariate mixed data. We model the distribution of the
texture features using a mixture of Gaussian distributions. Unlike most
existing clustering methods, we allow the mixture components to be
degenerate or nearly-degenerate. We contend that this assumption is
particularly important for mid-level image segmentation, where
degeneracy is typically introduced by using a common feature
representation for different textures in an image. We show that such a
mixture distribution can be effectively segmented by a simple
agglomerative clustering algorithm derived from a lossy data
compression approach. Using either 2D texture filter banks or simple
fixed-size windows as texture features, the algorithm effectively
segments an image by minimizing the overall coding length of the
feature vectors. We conduct comprehensive experiments to measure the
performance of the algorithm in terms of visual evaluation and a
variety of quantitative indices for image segmentation. The algorithm
compares favorably against other well-known image segmentation methods
on the Berkeley image database.

We provide the source codes that implement four standard image
segmentation indices that compare the difference between two
segmentation results of the same set of images. Particularly, we are
interested in comparing segmentation results between an algorithm and
human subjects.

The Probabilistic Rand Index (PRI)
[Pantofaru2005] counts
the fraction of pairs of pixels whose labellings are consistent between
the computed segmentation and the ground truth, averaging across
multiple ground truth segmentations to account for scale variation in
human perception.

The Variation of Information (VoI) metric
[Meila2005]
defines the distance between two segmentations as the average
conditional entropy of one segmentation given the other, and thus
roughly measures the amount of randomness in one segmentation which
cannot be explained by the other.

The Global Consistency Error (GCE)
[Martin2001] measures
the extent to which one segmentation can be viewed as a refinement of
the other. Segmentations which are related in this manner are
considered to be consistent, since they could represent the same
natural image segmented at different scales.

The Boundary Displacement Error (BDE)
[Freixenet2002]
measures the average displacement error of boundary pixels between two
segmented images. Particularly, it defines the error of one boundary
pixel as the distance between the pixel and the closest pixel in the
other boundary image.